This sample constructed response problem for grade 3-5 students provides an opportunity to analyze patterns and develop algebraic thinking in the context of a telephone chain. It includes suggestions for adjusting the challenge level and a task-specific rubric with annotated samples of student work at each level. Free registration allows users to download a 9-page print-friendly version (pdf).

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Contributed by: Exemplars, Publisher

This resource is included in the following PD Collection(s):CCSS Practice Standard 8The resources in this collection are intended to help educators understand and implement the eighth Mathematical Practice Standard of the CCSS. You will find informative presentations, lesson plans, and problem sets that will help establish mathematical habits of mind that support this standard. You'll also find many problem tasks for use with students in the companion classroom collection.

Construct viable arguments and critique the reasoning of others.[K-12]

Reason abstractly and quantitatively.[K-12]

Operations and Algebraic Thinking[K - 5]

Solve problems involving the four operations, and identify and explain patterns in arithmetic.[3]

8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.[3]

9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.[3]

Use the four operations with whole numbers to solve problems.[4]

3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.[4]

Generate and analyze patterns.[4]

5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.[4]

Analyze patterns and relationships.[5]

3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.[5]